#1,085 – Binary Floating Point Numbers

When we write decimal floating point numbers, digits to the left of the decimal point indicate values of powers of 10 (1, 10, 100) that should be summed together.  Digits to the right of the decimal point indicate values of negative powers of 10 (1/10, 1/100, etc).

We can also write binary floating point numbers.  Numbers represented this way aren’t seen very often in practice, but are important to understand when we talk about how to store floating point numbers in memory.

Digits to the left of the decimal point in a binary floating point number represent powers of 2 (1, 2, 4) to be summed together.

Digits to the right of the decimal point in a binary floating point number represent negative powers of two, e.g. 1/2, 1/4, 1/8, etc.

Here are some examples.